1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1 A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

A
$${2 \over 5}$$
B
$${2 \over 7}$$
C
$${1 \over 5}$$
D
$${7 \over 10}$$
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads$$-$$1).

A
$${M \over {(M + m)}}$$
B
$${{(M + 2m)} \over {2M}}$$
C
$${{2M} \over {(M + 2m)}}$$
D
$${{2(M + 2m)} \over M}$$
3
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1 A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $$\omega$$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $$\mu$$. The beaker will revolve with the disc if :

A
$$R \le {{\mu g} \over {2{\omega ^2}}}$$
B
$$R \le {{\mu g} \over {{\omega ^2}}}$$
C
$$R \ge {{\mu g} \over {2{\omega ^2}}}$$
D
$$R \ge {{\mu g} \over {{\omega ^2}}}$$
4
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?
A
18.75 kgm2
B
1.905 $$\times$$ 105 kgm2
C
19.05 kgm2
D
1.875 $$\times$$ 105 kgm2
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